Research
Research
In this project, developed with Prof. Kuehn, we explore how the classical ideas of the singular perturbation theory (GSPT) can be applied to fast-slow systems in infinite dimensions. Thereby, we develop new geometric techniques for the existence and persistence of slow manifolds in this setting. A first result for fast-reaction systems can be found in this article. We are also working on applying the abstract theory to problems from ecology or bio-chemical processes such as the SKT model or the Michaelis-Menten model.
Understanding the effects temperature and entropy have in fluid dynamics from both a modelling and analytical perspective was the focus of my PhD research under the supervision of Prof. Liu. In a series of papers we derived non-isothermal fluid models that are consistent with the second law of thermodynamics and used advanced tools from functional analysis to prove the existence (and uniqueness) of solutions.